Question

If \( a, b, c \) are in A.P. and if the equations \( (b - c)x^2 + (c - a)x + (a - b) = 0 \) and \( 2(c + a)x^2 + (b + c)x = 0 \) have a common root, then

• A. \( a^2, b^2, c^2 \) are in A.P.
• B. \( a^2, c^2, b^2 \) are in A.P.
• C. \( c^2, a^2, b^2 \) are in A.P.
• D. \( a^2, b^2, c^2 \) are in G.P.

Hint:

When equations share a common root, substitute the root and use the A.P. condition to simplify. Check the resulting sequence for A.P. or G.P.